Some time during the mid-1980s, he can't quite remember the date, Tony Bennett, then a crooner on the wane, had a revelation. It came to him, like it does to so many of us these days, via the medium of television.

"I was watching that music channel, MTV," he recalls, his eyes glazing at the memory, "and what I liked about it was that they showed, you know, videos." Watching videos, he says, taught him that what you could once do with audio alone you could now also do with film; you could describe a song with images. "I liked that. I said to my son Danny [who was by then managing his career] that we should do something like that. We should make videos." This he duly did, a series of them, Tony standing by the piano, smiling a 24-carat smile and singing in that mellifluous voice of his. "My career turned around as a result."

A decade later, MTV invited him to record one of their celebrated Unplugged concerts, in which esteemed rock, pop and, in this case, easy-listening artists performed largely acoustically in front of a handpicked audience that comprised, invariably, of young people in trainers and T-shirts.

"I introduced these people, these kids, to the Great American Songbook, to songs by the masters, and I mean Cole Porter, Ira Gershwin, Johnny Mercer. Friend, they never knew what hit them."

Unexpectedly reinvigorated, Bennett started selling records again. This was a distinct novelty for someone deep into his sixties. His son lined up guest appearances on hip US talk shows like The Late Show with David Letterman and Late Night with Conan O'Brien, and even got him immortalised on The Simpsons. By 1998, he was playing to a reverential, if partially stoned, crowd at a particularly muddy Glastonbury, his set a clear festival highlight.

All this, I say to him now, must have been a very pleasant surprise, to find that he was now suddenly cool and trendy again?

"A surprise? It wasn't a surprise at all," he says a little huffily, pushing his glasses high up on to his forehead. "And I'll tell you why. Good music is good music. I'm not concerned with whether someone who listens to me is old or young. In fact, in many ways, I'm not interested in the young at all. I'm interested in age. People learn to live properly when they get of an age, you know? The late Duke Ellington once said to me that he was really offended by the word 'category'. Music has no category; it's either good or it isn't, and I sing good songs, great songs, written by the best songwriters. It's that kind of quality that makes them last. Trust me, people will be singing these songs for ever."

Tony Bennett, living legend, is in London this month for two reasons. The first is to pick up a GQ magazine Inspiration Award (not, he believes, for his contribution to music so much as his services to style: "Do I spend a lot of money on suits? I do. But I'm worth it"), and also to launch his latest album, A Swingin' Christmas, in which he reinterprets some seasonal classics. Inevitably, this record – which, oddly, is released two months ahead of the time it is supposed to celebrate – is as cheesy as all Christmas records must by definition be, but Bennett equips himself throughout the melodious roasting of chestnuts on open fires in the manner for which he is rightly famed. His voice, now aged and oaky at 82, is still a wondrous thing, as comforting as Ovaltine is to grandma. And grandma is very likely to be a fan. "All my fans, particularly my British ones," he says, ever the charmer, "are like my extended family. I love them very much."

He is very possibly the last of a kind, Tony Bennett, and for the past 60 some years has been reinterpreting easy-listening standards over and over again, insisting that each time he comes to sing these eternally perfect songs – "Strangers in Paradise", "I Left My Heart in San Francisco" and "The Good Life" among them – he finds something new in them, and has thus endeared himself to at least 50 million record buyers to date. It was Bob Hope, so the story goes, who first discovered him way back when he was still trading under the stage name of Joe Bari, and it was Frank Sinatra who proclaimed him the greatest singer since, well, since Frank Sinatra. He has been musical royalty ever since.

Born Anthony Benedetto in Astoria, New York, in 1936 to Italian immigrants, he grew up in the grip of Depression-era America. When he was 10, his father died, leaving, he says now, "my mother to bring up three boys alone. She was a seamstress on just a penny a dress but she was a proud woman, with high standards even then. If ever they gave her a dress that wasn't up to scratch, she would throw it over her shoulder. It was she who taught me never to compromise, never to be tempted by the frivolous fancy of the moment, to strive instead for quality."

Clearly a mother's boy, he has remained true to her teachings ever since. Whenever in London, he likes to stay at the Dorchester, which is where we meet now, in a suite that positively hums with quality. It's the size of your average two-bedroom apartment and very likely as expensive as your average three-bedroom. He enters the room with slow-moving, elderly poise, dressed impeccably in his favourite Savile Row suit, and perches himself gingerly on an overstuffed sofa that looks as if it is expecting no less a posterior than the Queen's. Throughout our conversation, he will turn to look at the window in silence, as if lost in thought. And he very probably is. At his age, he tells me, it is difficult not to remain permanently reflective, and so whenever anyone asks him about his life, which I am doing now, he finds it difficult not to lose himself completely.

In many ways, Tony Bennett always was a man out of time. His favourite era of showbiz, he says, was vaudeville, which peaked before he was born, and all his favourite songwriters (the aforementioned Porter and Gershwin) reigned long before he ever picked up a microphone. A strictly commercial singer who first broke through in the Fifties, Bennett made Las Vegas his spiritual home for the better part of two decades, and though he befriended Sinatra, he resisted any temptation to join the Rat Pack because he was ultimately far too sensitive to hold his own in a room full of such tough guys. "They kept awfully long hours," he says with an enigmatic smile.

He was also to find himself increasingly at odds with the new music then sweeping the world: rock'n' roll. Of the Rolling Stones, he once said that their onstage behaviour prompted "juvenile delinquency".

"Rock music was always too loud for me," he complains. "It's not musical. To me music is Frank Sinatra, Ella Fitzgerald, it's gorgeous, a turn-on. But when there is shouting in music, when there is noise? I don't like it. And I've always hated rock concerts in stadiums. That kind of mass gathering reminds me of people imitating Hitler."

He feels a similar reproach towards most sporting occasions, and considers American football far too aggressive. "The only sport I do follow is tennis. Tennis is much more civilised, and civilisation is something I search for in everything, every day."

His inability ever to tailor his music to current tastes, meanwhile, didn't always work as well for him then as it does now. By the late Sixties, his record company considered him a spent force and insisted he get with the beat by recording an album of pop covers. The result, Tony Sings The Great Hits Of Today, was so dreadful that his response to it was to regurgitate. Literally.

"I threw up in the record company offices and walked out," he says. "And that was pretty much that."

Thus begun his lost years, which stretched into an entire decade. Throughout the Seventies, he battled a much-documented depression and mounting drug problems that culminated, in 1979, with a near-fatal overdose. But he refutes all such charges today.

"My lost years?" he says. "I didn't lose any years, friend. I went to paradise." By this he means that he relocated to the UK where he worked with the composer Robert Farnan, but the records they made together didn't sell. "That may be true, but I didn't care. I had taken a leave of absence. I painted, I sang, I made music. Like I said, paradise."

And what of the rumoured overdose?

"That's a lie; it never happened. Sure, I did maybe indulge in moderate drug use, but the whole country did back then. You have to remember that this was a time of Martin Luther King being assassinated, Bobby and Jack Kennedy too [though these events actually happened a decade and more before]. It really smashed America. The whole country went out and did things, we were devastated by what was happening to our people and so we ... we tried drugs. It's the same old routine: you start out on marijuana and then somebody hands you cocaine. If you keep going with that, you die. I stopped."

By the early Eighties, his son had come on board to rescue him from, among other things, looming bankruptcy. At the time, Danny Bennett was fronting his own band, Quacky Duck And His Barnyard Friends, which, it is probably fair to say, was hardly setting the music world alight. "But he had terrific business sense," his father says. "He saved me."

The resurrection of his career, which really took hold after his Glastonbury appearance, was neatly, if unwittingly, timed. Towards the end of the Nineties, easy listening was becoming increasingly popular again – Rod Stewart had begun his own interpretations of the Great American Songbook, to be followed later by Robbie Williams, Jamie Cullum and Michael Bublé – and so Danny shrewdly marketed his father as the genre's presiding godfather, its living Don. His 2006 album Duets: An American Classic featured songs with Elvis Costello, Sting, Bono and Paul McCartney. It was to prove one of his biggest chart successes.

Earlier this year, he was invited to appear on stage alongside Billy Joel at New York's Shea Stadium. He had never played a stadium before, chiefly because of that hatred of his: large crowds, Hitler-ish atmosphere. Nevertheless, he was overawed by the applause of 59,000 people.

"My son said to me afterwards that if I played just seven stadium shows a year then financially I wouldn't need to work on anything else outside that at all. I said to him, what a bore. I live to sing. Why on earth would I want to sing less."

Because of his advanced years, perhaps?

"Bah," is his response.

If anyone had it in him to write a truly enlightening, lid-lifting memoir on the golden years of American showbiz, then it is surely Tony Bennett. Recent reports suggest that Tony Curtis, Roger Moore and Christopher Plummer are all at it, shucking off their collective air of rarefied elegance to finally tell it as it is. They are all old now, is effectively the suggestion here, and so to hell with whoever they offend. But Bennett, who counted Cary Grant and Fred Astaire as close friends alongside many other Hollywood legends, the occasional mafioso and several presidents, feels no such temptation.

"So what if it would be popular?" he counters. "The National Enquirer is popular, so too was Hitler. I hate gossip."

He would, however, like to write a book on humanity.

"I care about humanity deeply. I would like to see an end to violence and war, and for there to be world peace." His eyes look very small behind his glasses, and his voice is tremulous. "Is that naïve of me?"

A lifelong pacifist, Bennett served for the Allies during the final bloody months of the Second World War. The experience left an indelible mark.

"It was 1944. We arrived in Germany and all I saw were dead soldiers everywhere, people having killed one another like animals. I never understood how you were supposed to take another's life, even if you had trained for it. When you are born, you are told that you must believe in God and that you must love your fellow man. So how can you then, all of a sudden, hate them and want to kill them? That was too schizophrenic for my mind. I couldn't take it in, and I didn't."

Bennett, a liberal Democrat, met George W Bush at a black-tie function back in 2005. I ask him whether he took the opportunity to have a go at him for Iraq. The question makes him uncomfortable.

"Well ... I don't really want to get into politics, if only because I love my country too much for that," he says haltingly. "But ultimately I do have a lot of faith in America. I think it's the greatest country in the world. I'm not simply flag-waving here, you understand, but we are the first country to have all different nationalities and religions in the one place. We are the ultimate melting pot. Sure, not everyone has learned to live with everyone else just yet, but we are still young and I believe we can progress."

Come November, he hopes his country will become more progressive still.

"Obama is a very great man. I think he will make a great leader."

Before he leaves, we talk about modern music and I ask him what, if anything, he makes of it. He responds by saying he has little time for it, and would much rather sit and paint instead (Bennett is a highly regarded artist, his watercolours exhibited in galleries around the world).

"Young singers today just don't have the experience," he says. "If you ask me, they could all use vaudeville training, otherwise we'll never have consummate performers ever again." They could also, he suggests, use singing lessons. "When I first heard Paul McCartney sing, I thought he had such a sweet sounding voice. But these days all people seem to do is screech and scream over one another."

He lets out an 82-year-old sigh, and spreads his hands helplessly wide.